Problem: Complete the square to solve for $x$. $x^{2}+10x+24 = 0$
Solution: Begin by moving the constant term to the right side of the equation. $x^2 + 10x = -24$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $10$ , half of it would be $5$ , and squaring it gives us ${25}$ $x^2 + 10x { + 25} = -24 { + 25}$ We can now rewrite the left side of the equation as a squared term. $( x + 5 )^2 = 1$ Take the square root of both sides. $x + 5 = \pm1$ Isolate $x$ to find the solution(s). $x = -5\pm1$ So the solutions are: $x = -4 \text{ or } x = -6$ We already found the completed square: $( x + 5 )^2 = 1$